Question

Let x denote the number of defective light bulbs in a randomly selected 20-count box from a local hardware store. The variable x has the following probability distribution:

x 0 1 2 3 4
P(X) 0.28 0.37 0.22 0.08 0.05

Calculate and interpret σx.

Answer 1

Step-by-step explanation:

First, find the expected value.

μ = 0 (0.28) + 1 (0.37) + 2 (0.22) + 3 (0.08) + 4 (0.05)

μ = 1.25

Now find the standard deviation.

σ² = (0−1.25)² (0.28) + (1−1.25)² (0.37) + (2−1.25)² (0.22) + (3−1.25)² (0.08) + (4−1.25)² (0.05)

σ² = 1.2075

σ = 1.099

If we were to select many boxes of bulbs randomly, the number of defective bulbs would typically vary about 1.099 from the mean.